The mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form φ (for some 0 ≤ p ≤ n) which is a calibration, meaning that:
φ is closed: dφ = 0, where d is the exterior derivative
for any x ∈ M and any oriented p-dimensional subspace ξ of TxM, φ|ξ = λ volξ with λ ≤ 1. Here volξ is the volume form of ξ with respect to g.Set Gx(φ) = { ξ as above : φ|ξ = volξ }. (In order for the theory to be nontrivial, we need Gx(φ) to be nonempty.) Let G(φ) be the union of Gx(φ) for x in M.
The theory of calibrations is...
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I've began to study the relationship between calibrations and holonomy, mainly through D.D. Joyce's Riemannian Holonomy Groups and Calibrated Geometry and partly through internet material.
Pretty much everyone explains this relationship by the holonomy principle: if $H=\text{Hol}_x$ and $\varp...
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I am new to computer vision and I have a problem which may not require a complex algorithm, however im not sure if I have enough data to ignore this.
problem statement:
I have a 6-joint robot arm and a 3D camera with trackers. With these trackers I can obtain the homogenous transformation matri...1
$u: \Omega \subset \mathbb R^2 \rightarrow \mathbb R$ is a $C^2$ function. Graph of $u$ is
$$
G_u=\{(x,y,u(x,y)) : (x,y)\in \Omega\}
$$
And the upward pointing unit normal is $N$. $\omega$ is the two-form on $\Omega\times \mathbb R$ given by that for $X,Y\in \mathbb R^3$
$$
\omega(X,Y) = \det (X...
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Rename calibrations to calibration-geometry.
The tag calibrations was created in June 2019. This is the question where the tag was created: Calibrations vs. Riemannian holonomy. From this question it seems that the intention was to created a tag for calibrated geometry. As the tag name can be in...
Proposal to remove (or even blacklist) significance
It is a meta tag and it is a bad one. I sincerely ask the creator to stop retagging old questions until we have an actual discussion.
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Rename calibrations to calibrated-geometry. (Also a name such as (calibrations-differential-geometry) - or something similar - would help with clarifying the content of the tag. However, that seems to be unnecessarily long.)
The tag calibrations was created in June 2019. This is the question whe...
